In this short conversation, Aveline will express her sympathy for Hawke's loss. In seeking to comfort Hawke, she offers to tell a story about her father. If you blame the Captain, or refuse to listen to her in a non-diplomatic way, there will be rivalry increases.

The choice to accept Aveline's offer to tell her father's story on the dialogue wheel is considered a "party member" action (see "Call on Companion" action on the dialogue page for more info). This means you must have Aveline in your current party to hear her tale about her father. Otherwise, only the options to decline are available. This is fixed in patch 1.03, but sometimes still occurs in 1.04.